In 3-4 sentences Compare and contrast adding/subtracting numbers written in scientific notation with multiplying/dividing numbers written in scientific notation. How are the steps in each case similar? How are they different? Do you think adding, subtracting, multiplying, or dividing numbers written in scientific notation is easiest? Why?

Answer 1

Adding and subtracting numbers in scientific notation requires that the numbers have the same exponent before performing the operation, leading to the adjustment of the coefficients as needed. In contrast, multiplying and dividing numbers in scientific notation involves manipulating the coefficients and exponents independently, where multiplication requires adding the exponents and division requires subtracting them. The similarities lie in the necessity to work with the coefficients and exponents, while the difference lies in the operations themselves—addition and subtraction focus on matching powers of ten, while multiplication and division leverage the properties of exponents. Many find multiplication and division easier due to the more straightforward processes of combining exponents rather than adjusting them to match, which can sometimes complicate addition and subtraction.